Expansive homeomorphisms of surfaces
- Cite this article as:
- Lewowicz, J. Bol. Soc. Bras. Mat (1989) 20: 113. doi:10.1007/BF02585472
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Letf be an expansive homeomorphism of a compact oriented surfaceM. We show thatS2 does not support such anf, and thatf is conjugate to an Anosov diffeomorphism ifM=T2, and to a pseudo-Anosov map ifM has genus ≥2. These results are consequences of our description of local stable (unstable) sets: everyx∈M has a local stable (unstable) set that consists of the union ofr arcs that meet only atx. For eachx∈Mr=2, except for a finite number of points, wherer≥3.